The analogy to this is that if you have a taut straight wire stretched between two fixed points, any force applied to the wire at about the center of it and at right angles to it will generate infinite tensile strain in the wire. Hence, universes can implode. See Calvin Lin
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Michael Mendrin
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2 years, 11 months ago

@John Muradeli
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In fact, quantum physics prohibit Newtonian infinitesimals of this sort that can create Newtonian infinities. One method experimental physicists use to generate extremely high pressures is to use a pointed diamond anvil, using the same logic as you've given here, i.e., given a finite force but an infinitesimal area, arbitrarily high pressures can be generated. But practical limits imposed by quantum physics does impose upper limits to pressures that can be created.

As for the wire example, the moment it stretches by any amount, there is no longer any "infinite tensile strain"---if it should stretch even by one atomic length.
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Michael Mendrin
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2 years, 11 months ago

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@Michael Mendrin
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oh no obviously I know that this can't happen practically. Even the shortest length (planck) is defined, so infinitesimality is out of question. But what I'm asking is, if this could be done, how could applying a force on the string (I still don't quite get the setup of the string) make the universe implode? Please share, because I simply love adding awesome infeasible facts to my list :D

@John Muradeli
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Oh, all right, maybe it will only crack up the planet, and the universe won't implode after all. But, in calculating the tensile force on the taut wire, if any force is applied to the wire cross-wise, the math is a lot like what you have above.

By the way, it might interest you that most of big bolts and screws are manufactured with "toggle-action cold heading machines", which operates on this principle in reverse. That is, there is a ram with a knuckle, so that when a force is applied on this knuckle, it achieves maximum ram force when the ram is straight. Also, there was the time I persuaded a cranky horse up in the mountains to move by tying the rope to a tree and then pushing on the rope. I think the horse was surprised that I was able to move him.
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Michael Mendrin
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2 years, 11 months ago